Problem: Simplify the following expression and state the condition under which the simplification is valid: $a = \dfrac{k^2 - 9k}{k^2 - 13k + 36}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{k^2 - 9k}{k^2 - 13k + 36} = \dfrac{(k)(k - 9)}{(k - 4)(k - 9)} $ Notice that the term $(k - 9)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(k - 9)$ gives: $a = \dfrac{k}{k - 4}$ Since we divided by $(k - 9)$, $k \neq 9$. $a = \dfrac{k}{k - 4}; \space k \neq 9$